Yes?

I did some research and found the following in a Q&A on this site. My question (at the very bottom) is whether the same rule applies to "e.g."

Q. Is it appropriate to add a semicolon before i.e. or e.g.? For example, is it correct to say “by focusing on prevention; i.e., identifying and intervening”?

Chicago: You can use a comma unless the material after the abbreviation starts a new independent clause.

She carried only the essentials, i.e., business cards, lipstick, pepper spray.

She saw to the last two details; i.e., flowers were waiting and the driver kept mum.

In either case a colon, an em dash, or parentheses might also work. And please note that Chicago doesn’t use i.e. or e.g. in running text (though we allow either in parentheses or notes). We use that is or a similar phrase. In many sentences (such as mine), you don’t really need the abbreviation; a colon or dash alone would be better.

That being said, would the same apply with "e.g."? That is, you can use a comma unless the material after the abbreviation starts a new independent clause.

Examples—are these correct?

{No independent clause follows "e.g."; hence, a comma is used before "e.g.," correct?}
He brought some of the essentials, e.g., a laptop, index cards, a stapler, and multiple reference sources.

{An independent clause follows "e.g."; hence, a semicolon is used before "e.g.," correct?}
He purchased some of the essentials that he needed for the project; e.g., he bought a laptop, index cards, a stapler, and several reference works.

Thank you.